Worksheet: Magnitude of a 2D Vector

In this worksheet, we will practice determining the magnitude of two-dimensional vectors.

Q1:

What is the magnitude of the vector 𝐴 𝐵 , where 𝐴 = ( 5 , 9 ) and 𝐵 = ( 9 , 1 ) ?

  • A 1 0
  • B4
  • C116
  • D 2 2 9
  • E 1 4

Q2:

What is the magnitude of the vector ?

Q3:

Given that , find the value of .

Q4:

What is the magnitude of the vector ( 4 , 5 ) ?

  • A 5
  • B 4
  • C1
  • D 4 1
  • E41

Q5:

Given that , find the value of .

  • A
  • B
  • C2
  • D
  • E10

Q6:

Given that , find the value of .

Q7:

What is the magnitude of the vector 𝐴 𝐵 where 𝐴 = ( 1 1 , 3 ) and 𝐵 = ( 7 , 3 ) ?

Q8:

How do you write the magnitude of a vector v ?

  • A m ( ) v
  • B [ ] v
  • C m a g ( ) v
  • D | | v
  • E ̂ v

Q9:

The vector is shown on the grid of unit squares below. Find the value of .

Q10:

The vector 𝑣 is shown on the grid of unit squares below. Find the value of 𝑣 .

Q11:

The vector is shown on the grid of unit squares below. Find the value of .

Q12:

What is the magnitude of the vector 𝐴 𝐵 , where 𝐴 = ( 9 , 1 3 ) and 𝐵 = ( 1 , 1 2 ) ?

  • A10
  • B101
  • C1
  • D 1 0 1
  • E 3 1 1

Q13:

What is the magnitude of the vector ?

Q14:

Given that 𝐴 = ( 2 , 1 4 ) , find 𝐴 .

  • A4
  • B200
  • C 3 2
  • D 1 0 2

Q15:

Given that 𝐴 = 5 𝑖 3 𝑗 , where 𝑖 and 𝑗 are two perpendicular unit vectors, find 𝐴 .

  • A 1 4
  • B 2 2
  • C 2 7
  • D 3 4

Q16:

What is the magnitude of the vector ?

Q17:

Find the magnitude of the vector shown on the grid of unit squares below.

Q18:

Find the magnitude of the vector shown on the grid of unit squares below.

  • A7
  • B50
  • C
  • D
  • E

Q19:

Find the magnitude of the vector shown on the grid of unit squares below.

Q20:

Consider the vectors u = 2 , 3 and v = 4 , 6 .

What is the magnitude of u ? Give your answer correct to two decimal places if needed.

What is the magnitude of v ? Give your answer correct to two decimal places if needed.

What is the magnitude of u v + ? Give your answer correct to two decimal places if needed.

Q21:

Given that , find the value of .

Q22:

The vector is shown on the grid of unit squares below. Find the value of .

  • A
  • B
  • C5
  • D
  • E9

Q23:

The vector is shown on the grid of unit squares below. Find the value of .

  • A
  • B
  • C13
  • D
  • E

Q24:

Find the magnitude of the vector shown on the grid of unit squares below.

Q25:

The vector is shown on the grid of unit squares below. Find the value of .

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